With the emergence of general foundational models, such as Chat Generative Pre-trained Transformer (ChatGPT), researchers have shown considerable interest in the potential applications of foundation models in the process industry. This paper provides a comprehensive overview of the challenges and opportunities presented by the use of foundation models in the process industry, including the frameworks, core applications, and future prospects. First, this paper proposes a framework for foundation models for the process industry. Second, it summarizes the key capabilities of industrial foundation models and their practical applications. Finally, it highlights future research directions and identifies unresolved open issues related to the use of foundation models in the process industry.